Related papers: A characterization of unbounded Fredholm operators

The main objective of the present article is to characterize regular Fredholm pairs and chains in terms of Fredholm operators.

In this paper we study the semi-Fredholm property of band-dominated operators $A$ and prove that it already implies the Fredholmness of $A$ in all cases where this is not disqualified by obvious reasons. Moreover, this observation is…

We characterize the groupoids for which an operator is Fredholm if, and only if, its principal symbol and all its boundary restrictions are invertible. A groupoid with this property is called {\em Fredholm}. Using results on the Effros-Hahn…

Let $A$ be a linear bounded operator in a Hilbert space $H$, $N(A)$ and $R(A)$ its null-space and range, and $A^*$ its adjoint. The operator $A$ is called Fredholm iff $dim N(A)= dim N(A^*):=n<\infty$ and $R(A)$ and $R(A^*)$ are closed…

Withdrawn due to a likely error with the homeomorphism at line (4). Old abstract: In the monograph 'Limit Operators and their Applications in Operator Theory', the authors define the operator spectrum of a band-dominated operator T and…

In this work characterizations of Fredholm pairs and chains of Hilbert space operators are given. Following a well-known idea of several variable operator theory in Hilbert spaces, the aforementioned objects are characterized in terms of…

We study the Spectral Analysis for a class of bounded linear operators T = D + F in a non Archimedean Hilbert space E, where D is a diagonal linear operator and where F is a finite rank linear operator. In this study of the Spectral…

This paper presents the Fredholm theory on l^p-spaces for band-dominated operators and important subclasses, such as operators in the Wiener algebra. It particularly closes several gaps in the previously known results for the case p=\infty…

In this paper, we define and index for continuous families of semi-Fredholm bounded liner operators. Moreover, we study various regularities and semiregularities of continuous families of bounded linear operators.

We describe two topologies on the space of unbounded Fredholm operators and we explain their K-theoretic relevance. In the process we also prove a very general result concerning the continuity of families of first order, elliptic boundary…

We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and include explicit formulas for all…

In this paper, we established Fredholm theory of the linearized ${{\bar \partial}}$-operator and studied the additivity of its index.

In this work it is introduced the notion of regular Fredholm pair, i.e. a Fredholm pair whose operators are regular. The main properties of these objects are studied, and what is more, they are entirely classified. Furthermore, the index of…

This paper has aim to characterize Fredholmness and Weylness of upper triangular operator matrices having arbitrary dimension n. We present various characterization results in the setting of infinite dimensional Hilbert spaces, thus…

We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit…

In this short paper we review and extract some features of the Fredholm Alternative problem .

Starting from the definition of A-Fredholm and semi-A-Fredholm operator on the standard module over a unital C*- algebra A, introduced in [8] and [4], we construct various generalizations of these operators and obtain several results as an…

We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The…

Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals.

We consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs…